Velocimetry is the process of providing instantaneous velocity vector measurements of a flow in a cross-section or volume. In fluid dynamics, measurements of velocity vector fields are important as it can be used to calculate derivative quantities such as rate of strain, and integral quantifies such as fluxes. Studying fluid mechanics is extremely challenging and complex as it involves interactions on the molecular and particle levels. Non-invasive tools that can help shed a light on flow behavior resulting from such interactions between flow components are very valuable. In many engineering problems, heat and mass transfer processes are strongly controlled by fluid motions. Understanding the fluid motion can help control such processes.
Computational Fluid Dynamics (CFD) techniques are often used to simulate flow behavior. However, those simulations do not completely capture the physical world and require a validation method through instantaneous visualization of fluid vector fields, including velocity.
There has been a variety of instruments used for measuring the velocity profile of a flow. For example Particle Doppler Velocimetry (PDV) and Particle Image Velocimetry (PIV) are two technologies for imaging velocity vector fields. Nevertheless, such instruments suffer from different shortcomings as many of them attempt to predict the velocity profile from following a few tracer particles. Moreover, the applicability of such techniques is often restricted to laboratory environment as used sensors are usually fragile.
Electrical Capacitance Tomography (ECT) has been applied to determine the velocity profile of multiphase flows. In these applications, twin plane ECT sensors were used to measure the velocity by cross-correlation between two 2D images from each ECT plane. However, the velocity profile found by this method is different from true flow velocity which can be quite complicated. This method is often restricted to measuring average velocity of a flow instead of mapping a vector velocity profile. Electrical Capacitance Volume Tomography (ECVT) has also been used to determine the velocity profile of a gas-solid fluidized bed by cross-correlation between successive two 3D images. Though still relying on cross-correlation, the ECVT based velocimetry has been the first successful effort to capture the true flow velocity as it is based on 3D volumetric imaging from which the volumetric velocity profile is calculated. However, cross-correlation of volume images poses two main obstacles: First, it is computationally intensive and cannot be applied for real-time velocity profiling applications. Second, the velocity profile lacks accuracy as any error from the image reconstruction process contaminates any subsequent calculations of velocity profiling based on cross-correlation since the images are used as inputs to the calculation process. The present invention provides a faster and more accurate method for velocimetry needed in many industrial applications.
A novel solution for velocity profile mapping is provided by the present invention. The proposed method is aimed at determining volumetric velocity profile of multiphase flows. It is based on ECVT and Adaptive ECVT (AECVT) sensors and uses the capacitive sensor sensitivity gradient to measure the velocity profile. Unique and salient aspects to this novel approach are: 1) the gradient of sensitivity distribution of an ECVT or AECVT capacitive sensor is used to extract velocity information from successive capacitance measurements directly; and 2) unlike velocimetry based on cross-correlation, the present approach requires only one three-dimensional (3D) reconstructed image. Consequently, the complexity of reconstruction of the present approach to determine the velocity profile is much lower than the cross-correlation velocimetry and similar to that of conventional ECT/ECVT/AECVT permittivity profile reconstruction (i.e., Linear Back Projection and Landweber Iteration).
The main steps of the system and method of the present invention are described as: 1) two successive capacitance measurements are taken from an ECVT or AECVT sensor that surrounds the flow vessel; 2) the time interval between the measurements is determined by the inverse of the frame rate of the data acquisition system; 3) from the capacitance measurements of the first frame, a 3D image is reconstructed using conventional volume tomography (e.g. Linear Back Projection and Landweber Iteration, or neural network based nonlinear technique, etc.) that gives the initial volumetric permittivity distribution inside the vessel; 4) the sensitivity gradient is calculated numerically from sensor sensitivity distribution and voxel dimensions; and 5) then, the data is put together, namely i) the time rate change of capacitance, ii) the initial permittivity distribution, and iii) the sensitivity gradient, with a novel algorithm based on Linear Back Projection, Landweber Iteration, or other commonly used reconstruction methods to yield a 3D velocity profile.